Percentile is not equivalent to percent, and I don't think the quoted text is using it in quite the right way (it's abusing the term Darwinism as well, but I guess that's for a separate question).
A percentage is simply a representation of a proportion out of 100. To say three out of every six is the same as to say fifty out of every hundred, in other words fifty percent (from the Latin per centum).
A percentile is a statistical measure of distribution. For a given set of data, it is the level below which a certain percentage of the data falls. In graphic terms, it represents the area under the curve of a distribution.
For a more human example, if you score in the 72nd percentile on an exam, it means you scored higher than 72 percent of all the people who took the same exam— regardless of what your actual score was. If your baby is in the 28th percentile for length, it means she is longer than 28 percent of all comparable babies (e.g. babies at a certain age).
Related terms include decile, quartile, and tertile, if you divide up your population by 10, 4, or 3 instead of 100.